is a 4x4 Area Magic Square with Vertical Lines (VL-AMS):
- the 16 entries are different natural numbers,
- the 4 rows, the 4 columns and the 2 diagonals sum up to the same result (=100).
- there exists a geometric square (with side length 20 here), which can be divided into 16 trapezoids by 3 vertical and 3 skew straight lines,
such that every VL-AMS entry is exactly the area of the corresponding trapezoid.
Observation 2 For every VL-AMS with smallest entry a und greatest entry N the magic sum is 2(N+a).
There are 8 pairs of entries with sum N+a. If both entries of such a pair are connected by a line, then the "connection figure" of the
VL-AMS is formed: the VL-AMS is a magic square of Dudeney Typ VI.|
Reflection at a vertical or horizontal central line or a 180 degree rotation of any VL-AMS results to a VL-AMS again.
|William Walkington:||Area Magic Squares of Order-4|
|Walter Trump:||Area Magic squares|